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In this work we develop a scalable computational framework for the solution of PDE-constrained optimal control under high-dimensional uncertainty.
Optimal control of systems governed by partial differential equations
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Exact and approximate controllability for distributed parameter systems
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Optimal control of two- and three-dimensional Navier-Stokes flow
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L. T. Biegler, O. Ghattas, M. Heinkenschloss, and B. van Bloemen Waanders, editors · 2003
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Investigation of the influence of the reynolds number on a plane jet using direct numerical simulation
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Goal-oriented, model-constrained optimization for reduction of large-scale systems
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Efficient Hessian calculation using automatic differentiation
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Hessian-based model reduction for large-scale systems with initial condition inputs
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M. Hinze, R. Pinnau, M. Ulbrich, and S. Ulbrich · 2008
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Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations
G. Rozza, D.B.P. Huynh, and A.T. Patera · 2008
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Lectures on Stochastic Programming: Modeling and Theory
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On the treatment of distributed uncertainties in PDE-constrained optimization
A. Borzì, V. Schulz, C. Schillings, and G. Von Winckel · 2010
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Randomized algorithms for estimating the trace of an implicit symmetric positive semi-definite matrix
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D. Bertsimas, D.B. Brown, and C. Caramanis · 2011
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Computational optimization of systems governed by partial differential equations
A. Borzì and V. Schulz · 2011
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Fast algorithms for Bayesian uncertainty quantification in large-scale linear inverse problems based on low-rank partial Hessian approximations
Pearl H. Flath, Lucas C. Wilcox, Volkan Akçelik, Judy Hill, Bart van Bloemen Waanders, and Omar Ghattas · 2011
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Error estimates of stochastic optimal neumann boundary control problems
M.D. Gunzburger, H.C. Lee, and J. Lee · 2011
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Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions
N. Halko, P-G Martinsson, and J.A. Tropp · 2011
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Finite element approximations of stochastic optimal control problems constrained by stochastic elliptic PDEs
L.S. Hou, J. Lee, and H. Manouzi · 2011
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An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach
Finn Lindgren, Håvard Rue, and Johan Lindström · 2011
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Efficient shape optimization for certain and uncertain aerodynamic design
C. Schillings, S. Schmidt, and V. Schulz · 2011
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Extreme-scale UQ for Bayesian inverse problems governed by PDEs
Tan Bui-Thanh, Carsten Burstedde, Omar Ghattas, James Martin, Georg Stadler, and Lucas C. Wilcox · 2012
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Analysis of the Hessian for inverse scattering problems. Part I: Inverse shape scattering of acoustic waves
Tan Bui-Thanh and Omar Ghattas · 2012
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Analysis of the Hessian for inverse scattering problems. Part II: Inverse medium scattering of acoustic waves
Tan Bui-Thanh and Omar Ghattas · 2012
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A trust-region algorithm with adaptive stochastic collocation for PDE optimization under uncertainty
D.P. Kouri, D. Heinkenschloos, M. Ridzal, and B.G. Van Bloemen Waanders · 2012
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Automated solution of differential equations by the finite element method: The FEniCS book
A. Logg, K.A. Mardal, and G. Wells · 2012
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A stochastic Newton MCMC method for large-scale statistical inverse problems with application to seismic inversion
James Martin, Lucas C. Wilcox, Carsten Burstedde, and Omar Ghattas · 2012
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Scalable and efficient algorithms for the propagation of uncertainty from data through inference to prediction for large-scale problems, with application to flow of the Antarctic ice sheet
Tobin Isaac, Noemi Petra, Georg Stadler, and Omar Ghattas · 2015
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Reduced basis approximation of parametrized optimal flow control problems for the Stokes equations
F. Negri, A. Manzoni, and G. Rozza · 2015
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Reduced Basis Methods for Partial Differential Equations: An Introduction
A. Quarteroni, A. Manzoni, and F. Negri · 2015
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Improved bounds on sample size for implicit matrix trace estimators
Farbod Roosta-Khorasani and Uri Ascher · 2015
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Progressive construction of a parametric reduced-order model for PDE-constrained optimization
M.J. Zahr and C. Farhat · 2015
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Stochastic collocation for optimal control problems with stochastic PDE constraints
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Analysis of the Hessian for inverse scattering problems. Part III: Inverse medium scattering of electromagnetic waves
Tan Bui-Thanh and Omar Ghattas · 2013
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A computational framework for infinite-dimensional Bayesian inverse problems Part I: The linearized case, with application to global seismic inversion
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Multilevel Monte Carlo analysis for optimal control of elliptic PDEs with random coefficients
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Hessian-based adaptive sparse quadrature for infinite-dimensional Bayesian inverse problems
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Reduced basis methods for uncertainty quantification
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A-optimal encoding weights for nonlinear inverse problems, with application to the Helmholtz inverse problem
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Analysis of the Hessian for optimization under uncertainty: Application to optimal design of acoustic metamaterial
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Hessian-based sampling for goal-oriented model reduction with high-dimensional parameter
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